On a fundamental description of the Kovacs' kinetic signatures in glass-forming systems.

The time-evolution equation for the time-dependent static structure factor of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory was used to investigate the kinetics of glass-forming systems under isochoric conditions. The kinetics are studied within the framework of the fictive temperature (TF) of the glassy structure. We solve for the kinetics of TF(t) and the time-dependent structure factor and find that they are different but closely related by a function that depends only on temperature. Furthermore, we are able to solve for the evolution of TF(t) in a set of temperature-jump histories referred to as the Kovacs' signatures. We demonstrate that the NE-SCGLE theory reproduces all the Kovacs' signatures, namely, intrinsic isotherm, asymmetry of approach, and memory effect. In addition, we extend the theory into largely unexplored, deep glassy state, regions that are below the notionally "ideal" glass temperature.

First-principles prediction of multiple stationary states in glass-forming liquids.

In the present work, the Non-Equilibrium Self-Consistent Generalized Langevin Equation (NESCGLE) theory is used to predict the final state of glass-forming liquids subjected to different cooling processes. We show that the NESCGLE theory correctly describes two essential features of the glass transition. Such features are the structural recovery and the dependence of the final state with the cooling rate. We demonstrate that below a particular temperature Tc, the system is unable to equilibrate, independently of the cooling rate. We show that the equilibrium state is only reached for the quasistatic process. Additionally, we show how, from the NESCGLE theory, it is possible to deduce a relaxation model of structural recovery, for which we obtain molecular expressions of the parameters.

Glass transition in soft-sphere dispersions.

The concept of dynamic equivalence among mono-disperse soft-sphere fluids is employed in the framework of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics to calculate the ideal glass transition phase diagram of model soft-sphere colloidal dispersions in the softness-concentration state space. The slow dynamics predicted by this theory near the glass transition is compared with available experimental data for the decay of the intermediate scattering function of colloidal dispersions of soft-microgel particles. Increasing deviations from this simple scheme occur for increasingly softer potentials, and this is studied here using the Rogers-Young static structure factor of the soft-sphere systems as the input of the SCGLE theory, without assuming a priori the validity of the equivalence principle above.

Glass-liquid-glass reentrance in mono-component colloidal dispersions.

The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics is employed to describe the ergodic-non-ergodic transition in model mono-disperse colloidal dispersions whose particles interact through hard-sphere plus short-ranged attractive forces. The ergodic-non-ergodic phase diagram in the temperature-concentration state space is determined for the hard-sphere plus attractive Yukawa model within the mean spherical approximation for the static structure factor by solving a remarkably simple equation for the localization length of the colloidal particles. Finite real values of this property signals non-ergodicity and determines the non-ergodic parameters f(k) and f(s)(k). The resulting phase diagram for this system, which involves the existence of reentrant (repulsive and attractive) glass states, is compared with the corresponding prediction of mode coupling theory. Although both theories coincide in the general features of this phase diagram, there are also clear qualitative differences. One of the most relevant is the SCGLE prediction that the ergodic-attractive glass transition does not preempt the gas-liquid phase transition, but always intersects the corresponding spinodal curve on its high-concentration side. We also calculate the ergodic-non-ergodic phase diagram for the sticky hard-sphere model to illustrate the dependence of the predicted SCGLE dynamic phase diagram on the choice of one important constituent element of the SCGLE theory.

Dynamic arrest within the self-consistent generalized Langevin equation of colloid dynamics.

This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.

Simplified self-consistent theory of colloid dynamics.

One of the main elements of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E 62, 3382 (2000); 72, 031107 (2005)] is the introduction of exact short-time moment conditions in its formulation. The need to previously calculate these exact short-time properties constitutes a practical barrier for its application. In this Brief Report, we report that a simplified version of this theory, in which this short-time information is eliminated, leads to the same results in the intermediate and long-time regimes. Deviations are only observed at short times, and are not qualitatively or quantitatively important. This is illustrated by comparing the two versions of the theory for representative model systems.